We can perceive position, velocity, acceleration, jerk

We can perceive position by establishing a reference point
We can perceive velocity by noticing a change in position
We can perceive acceleration by noticing a change in velocity
We can perceive jerk by noticing a change in acceleration

Can humans also perceive jounce or any higher order derivative of position? I'm trying to understand if it is actually possible or, if not, it is impossible due to human limitations?

To think about this you need to consider how the body gives the sense of those things. i.e. what does it feel like.

For instance - we do not "feel" our velocity by noting the change in position so much as from the wind in our faces and the vibration/sensation of movement.
The relative positions of things around us provide a clue though, especially for low speeds where the sense is sometimes fooled by small motions in the surrounding objects.

We feel accelerations as a pressure or a push, similar to gravity.
Motion simulators exploit this by tilting the simulator to simulate horizontal acceleration.
As before - visual cues reinforce this sensation (the simulator will also play a movie of an accelerating POV).

So what would a low continuous jerk feel like? - remember that this is the technical term not the common use word.
Well... it would feel like the direction and/or strength of gravity is slowly changing, but at a constant rate.
You'd probably spot that if you were looking for it, though you may interpret it as something else, like being slowly tilted back in your seat or as some viscous fluid impeding your limbs, depending of the visual cues.
Usually you can tell when you've made a transition between low and high acceleration though - especially if it is sudden.

To think about this you need to consider how the body gives the sense of those things. i.e. what does it feel like.

For instance - we do not "feel" our velocity by noting the change in position so much as from the wind in our faces and the vibration/sensation of movement.
The relative positions of things around us provide a clue though, especially for low speeds where the sense is sometimes fooled by small motions in the surrounding objects.

We feel accelerations as a pressure or a push, similar to gravity.
Motion simulators exploit this by tilting the simulator to simulate horizontal acceleration.
As before - visual cues reinforce this sensation (the simulator will also play a movie of an accelerating POV).

So what would a low continuous jerk feel like? - remember that this is the technical term not the common use word.
Well... it would feel like the direction and/or strength of gravity is slowly changing, but at a constant rate.
You'd probably spot that if you were looking for it, though you may interpret it as something else, like being slowly tilted back in your seat or as some viscous fluid impeding your limbs, depending of the visual cues.
Usually you can tell when you've made a transition between low and high acceleration though - especially if it is sudden.

You should be able to continue the reasoning to higher orders.

But there must still be a limit to how many derivatives we can perceive or take into account in our reasoning/thinking, because we are limited. Do we rely mostly on position, velocity and acceleration and consider a constant jerk to simplify things?

That is correct: there are many limits on our abilities.
You can continue the reasoning provided to discover where the limit lies in this case.

Do we rely mostly on position, velocity and acceleration and consider a constant jerk to simplify things?

It is difficult to know what you are asking here.

We rely on our sense of jerk (i.e. and for want of a better term) every day - almost every change in our motion involves non-constant accelerations.
Thus we are evolved to unconsciously account for a lot of non-linear processes: it is where a lot of our intuitions about motion come from.

The term "jerk" refers to a mathematical concept - invented to make thinking about motion easier, and easier to talk about... so it is a simplification in that sense.

When we do physics, as opposed to just walking down the street, we ask ourselves what is the least we need to know about something to still know everything about it.
The theory which gives the largest description with the least input is considered "simpler". This is why Newtonian Gravitation is simpler than Ptolemies Epicycles - they both work, but Newton's approach requires less foreknowledge and is more general.
Position, velocity, and acceleration (usually by way of forces), are all we need to know everything about the classical motion of a body.
These things are the simplification that our senses can only get through a more complicated series of impressions.

The bottom line is, in your work, you should "rely on" whatever it is that needs the least maths, and still gets you the right answer.